This application is based on Japanese Patent Application No. 2000-13029 filed Jan. 21, 2000, the content of which is incorporated hereinto by reference.
1. Field of the Invention
The present invention relates generally to a waveguide type optical circuit to be employed in construction of an optical communication system, an optical information processing system and so forth. More particularly, the invention relates to a technology effective in application for a no polarization wave dependent waveguide type optical circuit having no polarized wave dependency.
2. Description of the Related Art
Conventionally, associating with development of an optical communication technology, research and development has been made for various optical parts. Amongst, a waveguide type optical parts based on an optical waveguide on a flat substrate is the most important part. The reason is that the waveguides type optical part has a feature to be easily manufactured with high reproductivity achieving a precision less than or equal to an optical wavelength by a photolithographic technology and fine machining technology.
For example, a waveguide type Mach-Zehnder interferometer optical circuit is constructed with two optical couplers on the substrate and two connection waveguides connecting connecting these two optical coupler. By controlling optical path length difference and interference between two waveguide type phase condition, various functions can be realized. Such optical circuit has wide application fields, and has been put into practical use.
FIGS. 9A and 9B show an example of the conventional waveguide type Mach-Zehnder interferometer. FIG. 9A is a plan view and FIG. 9B shows a section taken along line IXBxe2x80x94IXB in FIG. 9A.
As shown in FIG. 9A, the Mach-Zehnder interferometer is constructed with a first input waveguide 23 and second input waveguide 24 formed in a clad 22 of a silicon substrate; 21, a first directional coupler 25 formed by placing the first input waveguide 23 and the second input waveguide 24 to be proximal with each other, a first output waveguide 26 and a second output waveguide 27, a second directional coupler 28 formed by placing the first output waveguide 26 and the second output waveguide 27 proximal with each other, first connecting waveguide 39 and second connecting waveguide 40 connecting the first directional coupler 25 and second directional coupler 28, and a thermo-optic phase shifter 41 (thin film heater) As a material for forming the optical waveguide, a fused silica prepared by way of flame hydrolysis deposition is used. As shown in FIG. 9B, the section is that a core having a section of 7 xcexcmxc3x977 xcexcm, for example the first connecting waveguide 39 and the second connecting waveguide 40, is embedded at substantially center portion of a clad 22 of 50 xcexcm thick deposited on the silicon substrate 21. A difference of refraction indexes of the clad and the core is 0.75%.
As the first directional coupler 25 and the second directional coupler 28, it is typical to employ 3 dB coupler set a branching ratio of 1:1. A light input from the input waveguide is equally divided by the first directional coupler 25 and propagated to the first connecting waveguide 39 and the second connecting waveguide 40. The light propagated to the first connecting waveguide 39 and the second connecting waveguide 40 are combined to cause mutual interference in the second directional coupler 28. The light combined by the second directional coupler 28 is variable of amont of light to be output to the first output waveguide 26 and the second output waveguide 27 respectively depending upon phase condition at that time. For example, when a light having a wavelength xcex from the first input waveguide 23 is equally divided by the first directional coupler 25 and combined in the second directional coupler 28, if the phase error of two lights is 0 or an integer multiple of the wavelength xcex, the combined light is output from the second output waveguide 27. On the other hand, when the phase error of the combined two lights is odd number multiple of the half-wavelength (xcex/2), the combined light is output from the first output waveguide 26. Furthermore, when the phase error of the combined light is the intermediate condition of the condition set forth above, namely when the phase error is neighter 0, integer multiple of the wavelength xcex nor odd number multiple of the half wavelength, the light is output from both of the first output waveguide 26 and the second output waveguide 27 at a ratio depending upon the instantaneous condition.
Assuming an optical path length difference between the first connecting waveguide 39 and the second connecting waveguide 40 is xcex94L, the Mach-Zehnder interferometer, as shown in FIG. 9A, in which the optical path length-difference xcex94L is 0 or approximately half wavelength of the wavelength of the light may operate as an optical attenuator or an optical switch by providing a thin film header operating as thermo-optic phase shifter 41 on the first connecting waveguide 39.
FIG. 10 is an illustration for explaining characteristics of the conventional Mach-Zehnder interferometer optical circuit, in which may operate thermo-optic phase shifter 41 in case of the optical path length difference xcex94L is 0. When thermo-optic phase shifter 41 may not operate, a light input from the first input waveguide 23 output from the second output waveguide 27. Thus, when the optical path length is effectively increased by heating the first connecting waveguide 39 by operating the thermo-optic phase shifter 41 (thin film heater) to increase refraction index of the first connecting wave guide 39 by thermo-optic effect, a part of the incident light from the first input waveguide 23 is output to the first connecting waveguide 39. When the optical path length difference xcex94L becomes half wavelength by adjusting a temperature of the first connecting waveguide 39, all of the incident light from the first input waveguide 23 is output to the first output waveguide 26. Thus, by variably adjusting the optical path length difference xcex94L of two connecting waveguides from 0 to have wavelength using the thermo-optic phase shifter 41, it becomes possible to operate as the optical attenuator. On the other hand, by using the optical path length difference xcex94L of two connecting waveguides only at 0 and half wavelength, it can be operated as special optical switch. An electrical power required for switching by the optical switch is about 0.5 W in case the thin film heater of 5 mm length and 50 xcexcm width. On the other hand, a temperature elevation of the thin film feature is about 30xc2x0 C.
The Mach-Zehnder interferometer optical circuit having the optical path length difference xcex94L of two connecting waveguides greater than or equal to several xcexcm, it can be operated as a wavelength filter. FIG. 11 is a plan view showing a general construction of the asymmetric Mach-Zehnder interferometer optical circuit. The asymmetric Mach-Zehnder interferometer optical circuit is constructed with the first input waveguide 23 and second input waveguide 24 fabricated on the clad 22 on the silicon substrate 21, a first directional coupler 25 formed by placing the first input waveguide 23 and the second input waveguide 24 to be proximal with each other, 1o the first output waveguide 26 and a second output waveguide 27, the second directional coupler 28 formed by placing the first output waveguide 26 and the second output waveguide 27 proximal with each other, first connecting waveguide 39 and second connecting waveguide 40 connecting the first directional coupler 25 and second directional coupler 28. As a material for forming the optical waveguide, a fused silica prepared by way of flame hydrolysis deposition is used. As shown in FIG. 9B, the section is that a core having a section of 7 xcexcmxc3x977 xcexcm, for example the first connecting waveguide 39 and the second connecting waveguide 40, is embedded at substantially center portion of a clad 22 of 50 xcexcm thick deposited on the silicon substrate 21. A difference of refraction indexes of the clad and the core is 0.75%. For example, among incident light from the first input waveguide 23, the light having wavelength, at which the optical path length difference xcex94L between the connecting waveguides is just 2N times (N is integer) of the wavelength, is output from the second output waveguide 27, and in case of 2(Nxe2x88x921) times, output from the first output waveguide 26. For example, when the optical path length difference xcex94L is about 1.48 mm it operates as a wavelength filter having a period of 200 GHz (1.6 nm in wavelength). FIG. 12 is a conceptual illustration of the wavelength characteristics in the case used as the wavelength filter.
Here, as shown in FIGS. 10 and 12, in case of the Mach-Zehnder interferometer optical circuit, the electric power of the thermo-optic phase shifter 41 and the switching power to obtain the same attenuation amount is variable depending upon condition of polarization of the incident light from the input waveguide, in the case of the optical attenuator or the optical switch having the optical path, length difference xcex94L of 0 or about half wavelength. In case of the wavelength filter having greater xcex94L, the period of the wavelength and the position of the peak (wavelength) are variable. This is the reason set forth below.
Namely, in case of the optical attenuator or the optical switch having the optical path length difference xcex94L of 0 or about half wavelength, it is the cause in that optical effect of the thermal stress generated by the thermo-optic phase shifter is differentiated depending upon respective polarization. More particularly, the foregoing is cased by the following mechanism. When the thermo-optic phase shifter is operated, the generated heat is diffused to the circumference, and tends to propagate in substance having high thermal conductivity. Thermal conductivity of air is 2.61xc3x9710xe2x88x924 W/(cm.deg), and thermal conductivity of the glass waveguide forming the Mach-Zehnder interferometer optical circuit is 0.014 W/cm.deg), and the thermal conductivity of the silicon substrate is 1.70 W/cm.deg), the heat generated in the thermo-optic phase shifter 41 is diffused mainly in the glass waveguide to be transmitted to the silicon substrate 21. Since the thermal conductivity of the silicon substrate 21 is quite high, the heat flows substantially perpendicularly to the silicon substrate 21 and a little heat is diffused to the circumference. Therefore, the connecting waveguide immediately below the thermo-optic phase shifter 41 is efficiently heated and the circumference thereof is locally expanded.
The glass waveguide is subject to large compression stress in horizontal direction with respect to the silicon substrate due to different of thermal expansion coefficients in comparison with the silicon substrate in the process of fabrication of the waveguide, in which the glass waveguide is once heated at a temperature higher than or equal to 1000xc2x0 C. and then cooled up to the normal temperature. Accordingly, the locally expanded peripheral portion of the connecting waveguide receives new compression stress from the silicon substrate in a direction parallel to the substrate. Therefore, in addition to variation of the refraction index due to temperature elevation, variation of the refraction index due to the compression stress is caused. Variation of the refraction index due to variation of the compression stress due is referred to as photoelastic effect and is expressed by the following equation (1).
xcex94nTE=(xcex94nx)=C1xcex94"sgr"xx+C2(xcex94"sgr"yy+xcex94"sgr"zz)
xcex94nTM=(xcex94ny)=C1xcex94"sgr"yy+C2(xcex94"sgr"xx+xcex94"sgr"zz)
Wherein x is a direction parallel to the silicon substrate, y is a direction perpendicular to the silicon substrate, z is a waveguide direction of the light, xcex94"sgr"xx, xcex94"sgr"yy, xcex94"sgr"zz are respective stress variation amount in x direction, y direction and z direction, in which tensile stress is expressed by positive value. xcex94nTE is a refraction index sensed by a light having electric field component in x direction parallel to the silicon substrate (hereinafter referred to as TE mode light), xcex94nTM is a refraction index sensed by a light having magnetic field component in x direction parallel to the silicon substrate (hereinafter referred to as TM mode light), C1 and C2 are photoelastic coefficient of fused silica, C1=xe2x88x920.74xc3x9710xe2x88x925 mm2xc2x7kg, C2=xe2x88x924.1xc3x9710xe2x88x925 mm2xc2x7kg.
As can be seen from the foregoing equation 1, when a compression stress is applied in a direction parallel to the silicon substrate, stress variation xcex94"sgr"xx is caused to increase refraction index of the glass waveguide, At this time, variation amount of the refraction index is different between the TE mode light and the TM mode light for difference of the photoelastic coefficients C1 and C2. Variation amount xcex94nTM of the TM mode light is greater than the variation amount xcex94nTE of the TE mode light. Namely, when the thermo-optic phase shifter 41 is driven, in addition to variation of refraction index due to thermo-optic effect, by variation of the refraction index due to local thermal stress, variation of the refraction index of the TM mode light becomes greater than that of the TE mode light so that optical variation of the TM mode light is progressed more quickly than the TE mode light. A drive power of the thermo-optic phase shifter 41 to have the same optical output is smaller than the TM mode light in the extent of about 4%. Accordingly, by employing the Mach-Zehnder.interferometer optical circuit having the optical path-length difference xcex94L of two connection waveguide as variable optical attenuator to attenuate the TE mode light for 10 dB, the TM mode light is attenuated about 11.5 dB to differentiate attenuation amount depending upon variation of polarization surface of the incident light of the optical attenuator.
On the other hand, in case of the Mach-Zehnder interferometer optical circuit having large the optical path length difference xcex94L of the connection waveguide, effective optical path length difference between the connection waveguide is expressed by the following equation (2):
xcex94L=xcex94lxc2x7n
In the foregoing equation 2, Al is a physical optical path length difference of the connection waveguide, n is the refraction index of the connection waveguide. Due to large compression stress in x direction exerted from the silicon substrate 21, the refraction index of the waveguide is expressed by the following equations (3)
nTE=n0+xcex94nTE
nTM=n0+xcex94nTM
In the foregoing equations (3), n0 is a refraction index of the waveguide when no stress is applied, xcex94nTE and xcex94nTM are respectively variation amount of refraction indexes of the TE mode and the TM modes due to stress obtained from the foregoing equation (1).
Comparing the variation amount xcex94nTe of refraction index of the TE mode light and the variation amount xcex94nTM of the refraction index of the TM mode light, the variation amount xcex94nTM of the refraction index of the TM mode light is greater. Therefore, the optical path length difference between the connection waveguides is effectively greater in the TM mode light than the TE mode light. When the optical circuit is employed as the wavelength filter, the wavelength xcex in outputting the incident light from the first input waveguide 23 to the second output waveguide 27 satisfies the following equation (4):
xcex94L=2Nxcex
wherein N is integer.
Since variation amount xcex94nTE of the refraction index of the TE mode light and the variation amount xcex94nTM of the refraction index of the TM mode light are different in values, the wavelength to be output is different depending upon polarization condition of the incident light. On the other hand, a difference xcex94xcex between the period the wavelength to output, namely wavelength to output and the shut off wavelength is expressed by the following equation (5):
xcex94xcex=xcex2/2nxcex94l
For example, assuming that the physical optical path length difference xcex94l of the connecting waveguide is 20.4 mm and the wavelength xcex of the incident light is 1.55 xcexcm, the period A of the wavelength becomes 0.4 nm from the foregoing equation (5). However, since the refraction index is different depending upon polarization condition, the period is differentiated depending upon the polarization condition. From these reason, even if a light of certain wavelength can be separated in the TE mode, for example, the TM mode light cannot be separated.
As a solution for this problem, there is a method to insert a half-wave plate at the center of two connection waveguides of the Mach-Zehnder interferometer optical circuit. By this, the incident light in the TE mode is converted into the TM mode at the intermediate position of the connection waveguide, and the incident light of TM mode is converted into TE mode. Therefore, for incident light of either polarization, the connection waveguide is effectively the same length. Therefore, polarization dependency can be resolved.
FIG. 13 shows an example of the no polarization dependent waveguide type Mach-Zehnder interferometer optical circuit resolving the polarization dependency by insertion of the half-wave plate. The Mach-Zehnder interferometer optical circuit shown in FIG. 13 is constructed with a first input waveguide 23 and second input waveguide formed in a clad 22 of a silicon substrate 21, the first output waveguide 26 and the second output waveguide 27, the first directional coupler 25 and the second directional coupler 28, first connecting wave guide 39A, first connecting wave guide 39B, second waveguide 40A, second waveguide 40B and thermo-optic phase shifter 41A and thermo-optic phase shifter 41B (thin film heater) and thin film type half-wave plate 32 inserted into the half-wave plate receptacle groove 31 formed at the center of the optical path of each connecting waveguide. As the first directional coupler 25 and the second directional coupler 28, 3 dB coupler is employed.
In fabrication of the half-wave plate receptacle groove 31, reactive ion etching or machining, such as dicing saw and so forth is employed. After insertion into the half-wave plate receptacle groove 31, the thin film type half-wave plate 32 is fixed by optical bond or the like. The half-wave plate may be a crystal, such as calcite. However, since the thickness becomes about 100 xcexcm including the glass substrate holding the crystal to have large loss. Therefore, it is typical to use the thin film type half-wave plate 32 as thin film provided birefringency by drawing a polyimide film. As a result, while loss is slightly increased, as optical characteristics of the Mach-Zehnder interferometer optical circuit, an average value of the TE mode light and the TM mode light as shown in FIGS. 10 and 12 is obtained to resolve polarization dependency.
While the foregoing description has been given for the Mach-Zehnder interferometer optical circuit, similar effect can be expected even in other circuit, such as arrayed waveguide grating optical circuit. FIG. 15 shows an example of no polarization dependency arrayed waveguide grating optical circuit resolving the polarization dependency. The arrayed waveguide grating optical circuit is constructed with an input waveguide cluster 34, a output waveguide cluster 36, a first slab waveguide 35, a second slab waveguide 37, the half-wave plate receptacle groove 31, the thin film type half-wave plate 32, a first arrayed waveguide 42A and a second arrayed waveguide 42B between the first slab waveguide 35 and the second slab waveguide 37.
The first arrayed waveguide 42A and the second arrayed waveguide 42B are provided a given optical path length difference xcex94L between adjacent waveguides. A light of certain wavelength incided from the input waveguide cluster 34 is diffracted at an inlet of the first slab waveguide 35 to spread in the first slab waveguide 35 and output to the first arrayed waveguide 42A. The light propagated to the first arrayed waveguide 42A and the second arrayed waveguide 42B reaches the second slab waveguide 37. However, since the given optical path length difference xcex94L is provided between adjacent waveguides in the arrayed waveguide, the light reaches the second slab waveguide 37 with a phase difference corresponding to the optical path length difference. The light entering into the second slab waveguide 37 is diffracted and spread. However, the light output from respective arrayed waveguides interfere with each other to diffract toward a direction (diffraction angle) where wave surface of light is arranged as a whole, to converge at a connecting portion with the output waveguide. By arranging the output waveguide at this position, the light of the wavelength set forth above can be branched. Since velocity of the light is variable depending upon wavelength, the phase difference provided by the arrayed waveguide is different to differentiate the convergence position depending upon the wavelength. Namely, the by connecting the output waveguide cluster 36 aggregating the output waveguides at the convergence position of the lights of respective wavelengths to the second slab waveguide 37, the lights of different wavelengths can be output from respective output waveguides.
Here, the effective optical path length difference xcex94L of the arrayed waveguide is different in the TE mode wave and the TM mode wave due to compression stress exerted by the silicon substrate. Accordingly, the wavelength output to certain output waveguide is differentiated by polarization condition. Therefore, by inserting the thin film type half-wave plate 32 at the intermediate position in the arrayed waveguide, the optical path length differences of the arrayed waveguide can be made equal for either polarized light.
The method for resolving polarization dependency by inserting the half-wave plate is a method applicable for other optical circuit, such as ring resonator, directional coupler and so forth.
However, in the prior art, in order to remove polarization dependency by the thin film type half-wave plate 32, the thin film type half-wave plate 32 has to be inserted strictly at the center of axial symmetry. Thus, it is typical to layout the optical circuit with maintaining axial symmetry. Accordingly, the half-wave plate receptacle groove 31 is formed perpendicularly with respect to respective connection waveguides. When the thin film type half-wave plate 32 is inserted in the half-wave plate receptacle groove 31 and fixed by optical bond, due to difference of refraction indexes between the glass waveguide and the optical bond and between the optical bond and the half-wave plate, a part of the light propagated through respective connection waveguides can be reflected to return toward the input waveguide side. Hereinafter, the light returning to the input waveguide side will be hereinafter referred to as reflected return light. For example, a spectrum of the reflected return light in the arrayed waveguide grating optical circuit shown in FIG. 15, is shown in FIG. 17. From FIG. 17, it can be seen that xe2x88x9235 dB of light at the maximum is reflected toward the incident port. The reflected return light can provide adverse effect for the system employing this device. For example, when the reflected return light returns to a semiconductor laser, an output intensity of he laser may be fluctuated to make the system unstable.
On the other hand, it is possible to reduce the reflected return light by obliquely forming the groove 31 for receiving the xcex/2 plate with respect to an axis of symmetry, as shown in FIGS. 14 and 16. However, in such case, the axial symmetry is destroyed to make it impossible to completely resolve the polarization dependency of the optical circuit.
The present invention has been worked out in view of the shortcoming set forth above. It is therefore an object of the present invention to provide a no polarization dependent waveguide type optical circuit which can completely resolve polarization dependency and can reduce reflected return light.
To achieve the above objective, the present invention according to a first aspect provides a no polarization dependent waveguide type optical circuit including one or more input waveguides formed on a substrate, a first optical coupler connected to the input waveguide, one or more output waveguides, a second optical coupler connected to the output waveguides, a plurality of connecting waveguide connecting the first optical coupler and the second optical coupler forming an optical circuit, and a polarization mode converter provided at a center of an optical path of the connecting waveguide of the optical circuit and converting a horizontally polarized light into a vertically polarized light and converting a vertically polarized light into a horizontally polarized light, wherein
intermediate portion of a plurality of the connecting waveguide being formed with S-shaped waveguides of the same shape consisted of respectively two curved waveguides.or two curved waveguides and straight waveguides connecting the curved waveguides, and
one or two polarization mode converters being provided in a groove formed across the S-shaped waveguide, and a perpendicular line to an incident surface of light of the polarization mode converter and the S-shaped waveguide forms an angle greater than 0xc2x0.
According to a second aspect, the invention provides a no polarization dependent waveguide type optical circuit provided with a polarization mode converter for converting a horizontally polarized light into a vertically polarized light and a vertically polarized light into a horizontally polarized light at a center of an optical path of connecting waveguides of a Mach-Zehnder interferometer optical circuit including a first directional coupler and a second directional coupler, in which two optical waveguides formed on a substrate are placed close proximity with each other, and two connecting waveguides connecting the first directional coupler and the second directional coupler, wherein
intermediate portion of the two connecting waveguide being formed with S-shaped waveguides of the same shape consisted of respectively two curved waveguides or two curved waveguides and straight waveguides connecting the curved waveguides, and
one or two polarization mode converters being provided in a groove formed across the S-shaped waveguide, and a perpendicular line to an incident surface of light of the polarization mode converter and the S-shaped waveguide forms an angle greater than 0xc2x0.
According to a third aspect, the invention provides a no polarization dependent waveguide type optical circuit provided with a polarization mode converter for converting a horizontally polarized light into a vertically polarized light and a vertically polarized light into a horizontally polarized light at a center of an optical path of connecting waveguides of a Mach-Zehnder interferometer optical circuit including a first multi-mode interference coupler and a second multi-mode interference coupler, in which two optical waveguides formed on a substrate are placed close proximity with each other, and two connecting waveguides connecting the first multi-mode coupler and the second multi-mode coupler, wherein
intermediate portion of the two connecting waveguide being formed with S-shaped waveguides of the same shape consisted of respectively two curved waveguides or two curved waveguides and straight waveguides connecting the curved waveguides, and
one or two polarization mode converters being provided in a groove formed across the S-shaped waveguide, and a perpendicular line to an incident surface of light of the polarization mode converter and the S-shaped waveguide forms an angle greater than 0xc2x0.
According to a fourth aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in the second or third aspect, a thermo-optic phase shifter is provided at least one of the connecting waveguides, and the thermo-optic phase shifter is separated on input side and output side of the polarization mode converter.
According to a fifth aspect, the invention provides a no polarization dependent waveguide type optical circuit including one or more input waveguides, a first slab waveguide, in which a light propagated through the input waveguide propagates freely, an arrayed waveguide consisted of a plurality of waveguides connected to the first slab waveguide and provided a given optical path length difference respective of adjacent waveguides, a second slab waveguide connected to the array waveguide and freely propagating the light propagated through the arrayed waveguide, and one of more output waveguide for forming an arrayed waveguide grating circuit, and a polarization mode converter converting a horizontally polarized light into a vertically polarized light and a vertically polarized light into a horizontally polarized light being provided in a center of an optical path of the arrayed waveguide of the arrayed waveguide grating circuit, wherein
intermediate portion of the arrayed waveguide being formed with S-shaped waveguides of the same shape consisted of respectively two curved waveguides or two curved waveguides and straight waveguides connecting the curved waveguides, and
one or two polarization mode converters being provided in a groove formed across the S-shaped waveguide, and a perpendicular line to an incident surface of light of the polarization mode converter and the S-shaped waveguide forms an angle greater than 0xc2x0.
According to a sixth aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in any one of the first to fifth aspect, the angle defined between perpendicular line to an incident surface of light of the polarization mode converter and the S-shaped waveguide is in a range of 3 to 10xc2x0.
According to a seventh aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in any one of the first to sixth aspect, the straight waveguide connecting the curved waveguides is tapered varying width in longitudinal direction, and the width of the tapered straight waveguide becomes maximum at a portion where the polarization mode converter is provided.
According to a eighth aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in any one of the first to seventh aspect, the polarization mode converter is a half-wave plate, an optical main axis of the half-wave plate forms 45xc2x0 relative to a waveguide substrate.
According to a ninth aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in any one of the first to eighth aspect, the polarization mode converter is a thin film type half-wave plate.
According to a tenth aspect, the invention provides a no polarization dependent waveguide type optical circuit wherein, in any one of the first to ninth aspect, the optical waveguide is a glass optical waveguide.
The above and other objects, features and advantages of the present invention will become more apparent from the following description of embodiments thereof taken in conjunction with the accompanying drawings.